Question

Create an Inequality with variables on both sides where the solution is x >-4​ A) 2x - 5 < 3x + 1

B) 3x + 2 < 4x - 2
C) x + 7 > 2x + 3
D) 4x - 3 ≤ 5x - 2

Answer 1

To create an inequality with variables on both sides and the solution x > -4, none of the given options are correct.

Step-by-step explanation:

To create an inequality with variables on both sides where the solution is x > -4, we need to adjust the given options and solve for x. Let's go through each option:

A) 2x - 5 < 3x + 1:

We subtract 2x from both sides to get -5 < x + 1. Subtracting 1 from both sides gives -6 < x, which is the same as x > -6. This does not match the solution x > -4, so option A is not correct.

B) 3x + 2 < 4x - 2:

We subtract 3x from both sides to get 2 < x - 2. Adding 2 to both sides gives 4 < x, which is the same as x > 4. This does not match the solution x > -4, so option B is not correct.

C) x + 7 > 2x + 3:

We subtract x from both sides to get 7 > x + 3. Subtracting 3 from both sides gives 4 > x, which is the same as x < 4. This does not match the solution x > -4, so option C is not correct.

D) 4x - 3 ≤ 5x - 2:

We subtract 4x from both sides to get -3 ≤ x - 2. Adding 2 to both sides gives -1 ≤ x, which is the same as x ≥ -1. This does not match the solution x > -4, so option D is not correct.

Since none of the given options matches the solution x > -4, there is no correct option.

Answer 2

C) x + 7 > 2x + 3 The chosen inequality, x + 7 > 2x + 3, accurately represents the conditions where x is greater than -4.

Step-by-step explanation:

The correct inequality is C) x + 7 > 2x + 3. To isolate the variable x on one side, you subtract x from both sides to move variables to the left side, leaving 7 > x + 3. To further isolate x, subtract 3 from both sides, yielding 4 > x or x < 4. However, since the initial inequality was x > -4, the solution remains x > -4. Therefore, the correct inequality satisfying x > -4 is x + 7 > 2x + 3. This inequality ensures the solution set where x is greater than -4.

This inequality transformation ensures that x remains greater than -4 while simplifying the equation step by step, adhering to the given conditions. Solving inequalities often involves isolating the variable to one side to determine the valid solution set, which in this case is x > -4.

This process maintains the relationship between the variables and constants in the original inequality while deriving the correct solution. The chosen inequality, x + 7 > 2x + 3, accurately represents the conditions where x is greater than -4.